A famous artist is auctioning off his masterpiece, which everyone values at $2:
There are two people who will bid, Alice and Bob. They have to put a whole dollar amount ($0, $1, $2, $3, ...) into an envelope (in secret).
Both the winner and loser will have to pay whatever they put in the envelope; the highest bidder will get the painting, while the loser won't receive anything. If there is a tie, the painting is given to one of them at random.
Assuming both people are trying to maximize their expected wealth, what would you if you were Alice?